Geodesic
Transformations of the transfinite plane
Forum of Mathematics, Sigma, Tome 9 (2021)

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We study the existence of transformations of the transfinite plane that allow one to reduce Ramsey-theoretic statements concerning uncountable Abelian groups into classical partition relations for uncountable cardinals.To exemplify: we prove that for every inaccessible cardinal $\kappa $, if $\kappa $ admits a stationary set that does not reflect at inaccessibles, then the classical negative partition relation $\kappa \nrightarrow [\kappa ]^2_\kappa $ implies that for every Abelian group $(G,+)$ of size $\kappa $, there exists a map $f:G\rightarrow G$ such that for every $X\subseteq G$ of size $\kappa $ and every $g\in G$, there exist $x\neq y$ in X such that $f(x+y)=g$. 
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     author = {Assaf Rinot and Jing Zhang},
     title = {Transformations of the transfinite plane},
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Assaf Rinot; Jing Zhang. Transformations of the transfinite plane. Forum of Mathematics, Sigma, Tome 9 (2021). doi: 10.1017/fms.2021.14

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